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Synthesis:
“Fundamental theorems of evolution”

Posted on January 23, 2017

David C. Queller

Is Fisher’s theorem uniquely fundamental? No – some others are just as fundamental, as judged by simplicity and scope

Abstract

Evolutionary biology is undergirded by an extensive and impressive set of mathematical models. Yet only one result, Fisher’s theorem about selection and fitness, is generally accorded the status of a fundamental theorem. I argue that though its fundamental status is justified by its simplicity and scope, there are additional results that seem similarly fundamental. I suggest that the most fundamental theorem of evolution is the Price equation, both because of its simplicity and broad scope and because it can be used to derive four other familiar results that are similarly fundamental: Fisher’s average excess equation, Robertson’s secondary theorem of natural selection, the breeder’s equation, and Fisher’s fundamental theorem. These derivations clarify both the relationships behind these results and their assumptions. Slightly less fundamental results include those for multivariate evolution and social selection. A key feature of fundamental theorems is that they have great simplicity and scope, which is often achieved by sacrificing perfect accuracy. Quantitative genetics has been more productive of fundamental theorems than population genetics, probably because its empirical focus on unknown genotypes freed it from the tyranny of detail and allowed it to focus on general issues.
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